{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:31:28Z","timestamp":1789392688169,"version":"build-2803163510"},"reference-count":42,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF\u20102020R1F1A1A01056987"],"award-info":[{"award-number":["NRF\u20102020R1F1A1A01056987"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Pharmaceutical Statistics"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Copula\u2010based survival regression models, which consist of a copula function and marginal distribution (i.e., marginal survival function), have been widely used for analyzing clustered multivariate survival data. Archimedean copula functions are useful for modeling such dependence. For the likelihood inference, one\u2010stage and two\u2010stage estimation methods have been usually used. The two\u2010stage procedure can give inefficient estimation results because of separate estimation of the marginal and copula's dependence parameters. The more efficient one\u2010stage procedure has been mainly developed under a restrictive parametric assumption of marginal distribution due to complexity of the full likelihood with unknown marginal baseline hazard functions. In this paper, we propose a flexible parametric Archimedean copula modeling approach using a one\u2010stage likelihood procedure. In order to reduce the complexity of the full likelihood, the unknown marginal baseline hazards are modeled based on a cubic M\u2010spline basis function that does not require a specific parametric form. Simulation results demonstrate that the proposed one\u2010stage estimation method gives a consistent estimator and also provides more efficient results over existing one\u2010 and two\u2010stage methods. The new method is illustrated with three clinical data sets. The Appendix provides an R function so that the proposed method becomes directly accessible to interested readers.<\/jats:p>","DOI":"10.1002\/pst.2153","type":"journal-article","created":{"date-parts":[[2021,8,3]],"date-time":"2021-08-03T06:52:18Z","timestamp":1627973538000},"page":"69-88","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Flexible parametric copula modeling approaches for clustered survival data"],"prefix":"10.1002","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0391-8170","authenticated-orcid":false,"given":"Sookhee","family":"Kwon","sequence":"first","affiliation":[{"name":"Department of Statistics Pukyong National University  Busan South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8434-9506","authenticated-orcid":false,"given":"Il Do","family":"Ha","sequence":"additional","affiliation":[{"name":"Department of Statistics Pukyong National University  Busan South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia\u2010Han","family":"Shih","sequence":"additional","affiliation":[{"name":"Institute of Statistical Science Academia Sinica  Taipei Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takeshi","family":"Emura","sequence":"additional","affiliation":[{"name":"Biostatistics Center Kurume University  Kurume Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,8,2]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1304-8"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-6557-6"},{"key":"e_1_2_10_4_1","doi-asserted-by":"crossref","unstructured":"EmuraT MatsuiS RondeauV.Survival Analysis with Correlated Endpoints; Joint Frailty\u2010Copula Models. 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